This paper introduces a real-time capable tension distribution algorithm for n degree-of-freedom cable-driven parallel robots (CDPR) actuated by n+2 cables. It is based on geometric considerations applied to the two-dimensional convex polytope of feasible cable tension distributions. This polytope is defined as the intersection between the set of inequality constraints on the cable tension values and the affine space of tension solutions to the mobile platform static or dynamic equilibrium. The algorithm proposed in this paper is dedicated to n degree-of-freedom cable-driven parallel robots (CDPR) actuated by n+2 cables. Indeed, it takes advantage of the two-dimensional nature of the corresponding feasible tension distribution convex polytope to improve the computational efficiency of a tension distribution strategy proposed elsewhere. The fast computation of the polytope vertices and of its barycenter made us successfully validate the real-time compatibility of the presented algorithm.